Method of transmitting information between a plurality of radioelectric stations and associated transmission network

ABSTRACT

A method of transmitting information between a plurality of radioelectric stations and an associated transmission network are disclosed. In one aspect, the method transmits information between radioelectric stations, each station including a transmitter and a receiver, the information including NbMot words of data, NbMot being an integer &gt;1. The transmission method includes: determining at least one polynomial of degree NbMot−1, each of the NbMot coefficients of the polynomial corresponding to a respective word, the polynomial having an indeterminacy, calculating NbRepet polynomial values for the polynomial, NbRepet being an integer &gt;1, each polynomial value being calculated for a respective predetermined value of the indeterminacy, transmitting the calculated polynomial values from one radioelectric station to at least one other radioelectric station, receiving polynomial values by the other radioelectric station, and determining, via the other radioelectric station, the NbMot words from a Lagrange interpolation of the received polynomial values.

INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

This application is a continuation of Application No. PCT/EP2013/069530,filed Sep. 19, 2013, which claims the benefit under 35 U.S.C. §119 ofFrench Application No. 12 02521, filed Sep. 21, 2012, which are hereinincorporated by reference in their entirety.

BACKGROUND

Field

The described technology generally relates to a method for transmittinginformation between a plurality of radioelectric stations, each stationcomprising a transmitter and a receiver, the information comprisingNbMot words of data, NbMot being an integer strictly greater than 1. Thedescribed technology also relates to a transmission network comprising aplurality of radioelectric stations.

Description of the Related Technology

The described technology in particular relates to the case where theinformation to be transmitted has a size larger than the size of a radiopacket dedicated to transporting that information. The describedtechnology also relates to the case where it is necessary to repeat thesending of the information several times in order to guarantee, with ahigh likelihood, the minimum likelihood depending on the desired qualityof service and for example equal to 0.99, the correct reception of atleast one copy of said information.

The described technology in particular applies to a transmission networkworking by frequency hopping in a predetermined frequency plane, thefrequency used for the data transmission being kept during a plateau,called a frequency hopping (FH) plateau, and changing from one FHplateau to another according to a frequency change law.

A transmission method of the aforementioned type is standard. Theinformation to be transmitted is conveyed in a frame comprising NbMotdata words T₁, . . . , T_(NbMot), and defined as follows:

[T₁∥T₂∥ . . . ∥T_(NbMot)], where ∥ symbolizes a data concatenation.

The transmission of the frame is repeated several times in order toguarantee, with a high likelihood, the correct reception of at least onecopy of the information. The transmission method comprises asynchronization mechanism between frames, to allow the receiving stationto identify each transmitted frame correctly.

Due to the repetition, one of the NbMot words of the frame, such as thefirst word T1, also contains a frame indicator TPS, said indicator TPSevolving over the course of the repetitions and making it possible tonumber the frames successively transmitted.

A synchronization information then comprises the synchronizationmechanism so that the receiving station recognizes the division intoframes and the frame indicator TPS. Upon each repetition of the frame,the value, denoted TPS(i), of the frame indicator TPS evolves such thatthe receiving station globally knows how to position the receivedpacket.

The transmitting station then transmits the data words T₁, . . . ,T_(NbMot) in different packets as follows:

-   -   packet number 1 containing the first word T₁ with the frame        indicator with value TPS(1),    -   packet number 2 containing the second word T2, . . . ,    -   packet number NbMot containing the word TNbMot, the packets        numbered 1 to NbMot forming the first frame,    -   packet number NbMot+1 containing the first word T₁ with the        frame indicator with value TPS(2),    -   packet number NbMot+2 containing the second word T₂, . . . ,    -   packet number 2×NbMot containing the word T_(NbMot), the packets        numbered NbMot+1 to 2×NbMot forming the second frame,    -   packet number 2×NbMot+1 containing the first word T₁ with the        frame indicator with value TPS(3),    -   packet number 2×NbMot+2 containing the second word T₂, . . . ,        and so forth up to a maximum number of frames, defined as a        function of a likelihood that the receiving station will        correctly obtain each of the data words T₁, . . . , T_(NbMot),        that likelihood also being called quality of service.

The word T₁ with the frame indicator whose value TPS(i) evolves isrepeated via packets having a number adjacent to 1 modulo NbMot.Likewise, the word T₂ is sent in packets having a number adjacent to 2modulo NbMot, and so forth. The word T_(NbMot) is repeated in packetshaving a number adjacent to 0 modulo NbMot.

Consequently, for the receiving station to obtain a copy of each wordT₁, . . . , T_(NbMot), it must be able to correctly decode NbMot packetsnot necessarily belonging to the same frame, but each having a differentnumber considering it modulo NbMot.

However, with such a transmission method, the maximum number of framestransmitted in order to guarantee the desired quality of service ishigh, and the transmission network is then particularly slow to transmitinformation.

SUMMARY OF CERTAIN INVENTIVE ASPECTS

One inventive aspect is a transmission method and network making itpossible to reduce the quantity of data transmitted by the transmittingstation to the receiving station(s), to convey said informationcomprising the data words T₁, . . . , T_(NbMot), while offering the samequality of service.

Another aspect is a transmission method of the aforementioned type,wherein the method comprises the following steps:

-   -   determining at least one polynomial of degree NbMot−1, each of        the NbMot coefficients of the polynomial corresponding to a        respective word, each polynomial having a variable,    -   calculating NbRepet polynomial values for each polynomial,        NbRepet being an integer strictly greater than 1, each        polynomial value being calculated for a respective predetermined        value of the variable,    -   transmitting the calculated polynomial values from one        radioelectric station to at least one other radioelectric        station,    -   receiving polynomial values by each other radioelectric station,        and    -   determining, via each other radioelectric station, the NbMot        words from a Lagrange interpolation of the received polynomial        values.

According to other advantageous aspects, the transmission methodcomprises one or more of the following features, considered alone oraccording to all technically possible combinations:

-   -   each word is divided into a plurality of patterns, and several        polynomials are determined using the following equation:

${P_{w}(X)} = {\left( T_{NbMot} \right)_{w} + {\sum\limits_{j = 1}^{{NbMot} - 1}{\left( T_{j} \right)_{w} \times X^{j}}}}$

with NbMot>1, 0≦w≦v and v≧1 and X designating the variable;

-   -   NbRepet data packets are successively transmitted during the        transmission step;    -   the packets are defined as follows:        Paquet(i)=P ₀((α₀)^(NbRepet-1-i))∥ . . . ∥P        _(w)((α_(w))^(NbRepet-1-i))∥ . . . ∥P        _(v)((α_(v))^(NbRepet-1-i))

with NbRepet>1, 0≦i≦NbRepet−1, 0≦w≦v;

(α_(w))^(NbRepet-1-i) designating the predetermined respective value ofthe variable to calculate the corresponding polynomial value, and

∥ symbolizing a data concatenation;

-   -   the method further comprises a step for calculating, via each        station receiving said packets, time synchronization information        for time synchronizing with the radioelectric station        transmitting said packets, from polynomial values received and        reception time deviations between the different received        packets;    -   the NbMot data words have a same size equal to N bits, N being        an integer strictly greater than 1;    -   one word among the NbMot data words comprises k bit(s) having a        predetermined constant value, k being an integer with 1≦k≦N;    -   each word comprises at least one pattern, and each pattern        represents an element of a mathematical field, such as a Galois        field;    -   each respective predetermined value, for which a polynomial        value is calculated, is a primitive element of said Galois        field.

Another aspect is a network for transmitting information, the networkcomprising a plurality of radioelectric stations, each stationcomprising a transmitter and a receiver, the information comprisingNbMot data words, NbMot being an integer strictly greater than 1,

wherein each station designed to transmit the information furthercomprises:

-   -   first means for determining at least one polynomial of degree        NbMot−1, each of the NbMot coefficients of the polynomial        corresponding to a respective word, each polynomial having a        variable,    -   first means for calculating NbRepet polynomial values for each        polynomial, NbRepet being an integer strictly greater than 1,        each polynomial value being calculated for a respective        predetermined value of the variable, and    -   means for transmitting the calculated polynomial values to at        least one other radioelectric station,

and in that each station designed to receive the information furthercomprises:

-   -   means for receiving polynomial values, and    -   second means for determining the NbMot words from a Lagrange        interpolation of the received polynomial values.

According to another advantageous aspect, the transmission networkcomprises the following feature:

-   -   each station designed to receive the information further        comprises a second means for calculating time synchronization        information for time synchronizing with the station designed to        transmit the information, from the received polynomial values        and reception time deviations between different received data        packets, NbRepet data packets being able to be successively        transmitted by the station intended to transmit the information.

BRIEF DESCRIPTION OF THE DRAWINGS

The features and advantages of the described technology will appear uponreading the following description, provided solely as a non-limitingexample, and done in reference to the appended drawings, in which:

FIG. 1 is a diagrammatic illustration of a radioelectric station of atransmission network according to an embodiment.

FIG. 2 is a diagrammatic illustration of the information to betransmitted comprising NbMot data words, NbMot being an integer strictlygreater than 1.

FIG. 3 is a diagrammatic illustration of the successive transmission ofNbRepet data packets, NbRepet being an integer strictly greater than 1.

FIG. 4 is a flowchart of a method for transmitting information accordingto an embodiment.

DETAILED DESCRIPTION OF CERTAIN INVENTIVE EMBODIMENTS

A transmission network according to an embodiment comprises a pluralityof radioelectric stations or radio stations 10, and is for example ableto operate by frequency hopping. A radioelectric station 10 isillustrated in FIG. 1.

The transmission network is able to transmit, from one radioelectricstation 10 to another radioelectric station 10, information, visible inFIG. 2, comprising NbMot data words T₁, T₂, . . . , T_(NbMot), NbMotbeing an integer strictly greater than 1. The radioelectric station 10designed to transmit the information is hereinafter called thetransmitting station, and the or each radioelectric station 10 designedto receive the information is hereinafter called the receiving station.

The set of frequencies usable by the transmission network comprises afrequency plane, also called an FH plane, for the frequency hoppingoperation. The FH plane for example belongs to the high frequency (HF)domain, between about 1.5 MHz and about 30 MHz. The FH plane is forexample a predetermined frequency plane.

The number of radioelectric stations 10 is for example greater than orequal to three, each station 10 being able to transmit data inconference to the other stations 10 of the network.

As shown in FIG. 1, each station 10 comprises a transmission-receptionchain 12, an antenna 14, a frequency synthesizer 16 and a processingunit 18.

The transmission-reception chain 12 is connected to thetransmission-reception antenna 14, the frequency synthesizer 16 and theprocessing unit 18, the frequency synthesizer 16 and the processing unit18 also being connected to each other.

The transmission-reception chain 12 comprises a device 20 for receivingradioelectric signals from the antenna 14 and a device 22 fortransmitting radioelectric signals to the antenna 14. Thetransmission-reception chain 12 can be controlled in a known manner bythe frequency synthesizer 16.

The processing unit 18 comprises an analog-digital converter 24connected at the output of the reception device 20 of thetransmission-reception chain, a microprocessor 26 connected at theoutput of the analog-digital converter 24, and a memory 28 connected tothe microprocessor 26.

The analog-digital converter 24 is able to convert the voltage orcurrent level provided by the reception device 20 into digital signalsamples transmitted to the microprocessor 26.

The microprocessor 26 is connected to the frequency synthesizer 16 andthe transmission-reception chain 12 for the transmission ofradioelectric signals intended for other transmitters-receivers 10 ofthe transmission network.

In the described embodiment, each station 10 is configured to operatealternatively as a transmitting station and a receiving station.

For the operation of the station 10 as a transmitting station, thememory 28 is able to store a first software 30 for determining at leastone polynomial P_(w)(X), 0≦w≦v, of degree NbMot−1, each of the NbMotcoefficients of the polynomial corresponding to a respective word, eachpolynomial having a variable X. The memory 28 is able to store a firstprogram 32 for calculating NbRepet polynomial valuesP_(w)((α_(w))^(NbRepet-1-i)), 0≦w≦v, 0≦i≦NbRepet−1, for the or eachpolynomial P_(w)(X), NbRepet being an integer strictly greater than 1,each polynomial value P_(w)((α_(w))^(NbRepet-1-i)) being calculated fora respective predetermined value (α_(w))^(NbRepet-1-i) of the variableX. The memory 28 is also able to store a transmission program 34,intended for at least one other radioelectric station 10, fortransmitting the calculated polynomial valuesP_(w)((α_(w))^(NbRepet-1-i)).

For the operation of the station 10 as a receiving station, the memory28 is able to store a software 36 for receiving said polynomial valuesP_(w)((α_(w))^(NbRepet-1-i)) transmitted by a transmitting station 10, asecond software 38 for determining the NbMot words T₁, T₂, . . . ,T_(NbMot) from a Lagrange interpolation of the received polynomialvalues P_(w)((α_(w))^(NbRepet-1-m)).

The transmission method is for example carried out during asynchronization phase between several radioelectric stations 10. Thesynchronization phase corresponds to the transmission of a burst ofelementary radio packets, i.e., a fixed number of elementary radiopackets. The synchronization procedure is used primarily to transmit twotypes of information between the transmitting station and the receivingstation, i.e., a technical datum necessary to decode the information anda time synchronization information t_final, the technical datum forexample comprising the address of the transmitter, the address of therecipient, the type of data transmission services, security data, suchas an integrity pattern, and cryptographic authentication. The timesynchronization information allows the receiving station to positionitself in the burst of received packets and to unambiguously deduce thestart time of the transmission phase of the information that follows thesynchronization phase.

Additionally, the memory 28 is able to store a second software 40 forcalculating the time synchronization information t_final with thetransmitting station 10, from the received polynomial valuesP_(w)((α_(w))^(NbRepet-1-m)) and reception time deviations betweendifferent received data packets Rm, with m an integer such that0≦m≦NbMot−1, NbRepet data packets Paquet(i), 0≦i≦NbRepet−1, being ableto be successively transmitted by the transmitting station 10.

Alternatively, each station 10 is configured to operate only as atransmitting station or only as a receiving station. The memory 28 ofthe transmitting station 10 then only comprises the first determinationsoftware 30, the first calculation software 32 and the transmissionsoftware 34. The memory 28 of each receiving station 10 then onlycomprises the reception software 36 and the second determinationsoftware 38. Additionally, the memory 28 of each receiving station 10comprises the second calculation software 40.

Alternatively, the first determination means 30, the first calculationmeans 32, the transmission means 34, the reception means 36, the seconddetermination means 38 and the second calculation means 40 are in theform of programmable logic components, or in the form of dedicatedintegrated circuits.

The method for transmitting the information will now be described inlight of FIGS. 2 to 4, FIG. 4 in particular illustrating a flowchart ofthe transmission method.

During step 100, the transmitting station 10 uses the firstdetermination software 30 to determine at least one polynomial P_(w)(X),0≦w≦v, of degree NbMot−1, each of the NbMot coefficients of thepolynomial P_(w)(X) corresponding to a respective word T₁, . . . ,T_(NbMot). The or each polynomial P_(w)(X) comprises a variable X, thevariable X preferably being unique for the or each polynomial P_(w)(X),where w and v are integers.

Each word T₁, . . . , T_(NbMot) comprises at least one pattern(T_(j))_(w), 0≦w≦v, j being an integer such that 1≦j≦NbMot, and the oreach pattern (T_(j))_(w) represents an element of a mathematical field,such as the Galois field.

The NbMot data words T₁, T₂, . . . , T_(NbMot) for example have the samesize equal to N bits, N being an integer strictly greater than 1.

In the described example, one word, such as the first word T₁, among theNbMot data words T₁, T₂, . . . , T_(NbMot) comprises k bit(s) having apredetermined constant value CST, k being an integer with 1≦k≦N, kdesirably being strictly greater than 1 and also such thatNbRepet−1<2^(k).

The k bits equal to CST for example represent an element of the Galoisfield GF(2^(k)). Out of a concern for homogeneity with the rest of thedescription, k is denoted a(0) such that GF(2^(k)) is equal toGF(2^(a(0))). α₀ is a primitive element of the Galois field))GF(2^(a(0))). The N-k other bits of the first word T₁ represent thesuccession of v elements respectively belonging to v bodies with formGF(2^(a(1))), . . . , GF(2^(a(v))), v being an integer greater than orequal to 1, such that

-   -   for any w, 1≦w≦v, a(w)≧k,

$\begin{matrix}{{\sum\limits_{w = 1}^{v}{a(w)}} = {N - k}} & (1)\end{matrix}$

In the specific case where v is equal to 1, the N-k bits represent anelement of the field GF(2^(N-k)).

α₁, . . . , α_(v) represent the v respective primitive elements of the vsuccessive Galois bodies GF(2^(a(1))), . . . , GF(2^(a(v))).

In the described example embodiment, each word T_(j), 1≦j≦NbMot, isdivided into v+1 patterns (T_(j))_(w), 0≦w≦v, v being greater than orequal to 1, each pattern (T_(j))_(w) being an element of a respectivefield GF(2^(a(j))). Each word T_(j) is then represented as follows:T _(j)=(T _(j))₀∥(T _(j))₁∥(T _(j))₂∥ . . . ∥(T _(j))v  (2)

In the particular case where the k first bits of the first word T1 areequal to CST, we also have: (T₁)₀=CST.

The first determination software 30 then determines several polynomialsP_(w)(X), 0≦w≦v and v≧1, using the following equation:

$\begin{matrix}{{P_{w}(X)} = {\left( T_{NbMot} \right)_{w} + {\sum\limits_{j = 1}^{{NbMot} - 1}{\left( T_{j} \right)_{w} \times X^{j}}}}} & (3)\end{matrix}$

with NbMot>1, 0≦w≦v and v≧1 and X designating the variable.

In the described example embodiment, the coefficients of each polynomialP_(w)(X) belong to the Galois field GF(2^(a(w))). Each of the NbMotcoefficients (T_(j))_(w) of the polynomial P_(w)(X) then corresponds toa respective pattern.

More specifically, the first determination software 30 then determinesthe v+1 following polynomials:

$\begin{matrix}{{{{{{{{{{P_{0}(X)} = {\left( T_{NbMot} \right)_{0} + {{CST} \cdot X} + {\left( T_{2} \right)_{0} \cdot X^{2}} + \ldots +}}\quad}\left( T_{{NbMot} - 1} \right)_{0} \times X^{{NbMot} - 1}}{{P_{1}(X)} = {\left( T_{NbMot} \right)_{1} + {\left( T_{1} \right)_{1} \cdot X} + {\left( T_{2} \right)_{1} \cdot X^{2}} + \ldots +}}}\quad}\left( T_{{NbMot} - 1} \right)_{1} \times X^{{NbMot} - 1}}\mspace{79mu}\ldots{{P_{v}(X)} = {\left( T_{NbMot} \right)_{v} + {\left( T_{1} \right)_{v} \cdot X} + {\left( T_{2} \right)_{v} \cdot X^{2}} + \ldots +}}}\quad}\left( T_{{NbMot} - 1} \right)_{v} \times X^{{NbMot} - 1}} & (4)\end{matrix}$

During step 110, the transmitting station 10 uses the first calculationsoftware 32 to determine NbRepet polynomial valuesP_(w)((α_(w))^(NbRepet-1-i)), 0≦w≦v, 0≦i≦NbRepet−1, for the or eachpolynomial P_(w)(X), i being an integer, NbRepet being an integerstrictly greater than 1. Each polynomial valueP_(w)((α_(w))^(NbRepet-1-i)) is calculated for a respectivepredetermined value of the variable X.

Each respective predetermined value for which a polynomial valueP_(w)((α_(w))^(NbRepet-1-i)) is calculated is, for example, theprimitive element (α_(w))^(NbRepet-1-i), 0≦w≦v, 0≦i≦NbRepet−1, of arespective Galois field GF(2^(a(w))).

The calculation of the polynomial value P₀((α₀)^(NbRepet-1-i))corresponds to calculations in the Galois field GF(2^(a(0))), i.e., inGF(2^(k)). The calculation of the polynomial valueP₁((α₁)^(NbRepet-1-i)) corresponds to calculations in the Galois fieldGF(2^(a(1))), and so forth.

During step 120, the transmitting station 10 next uses the transmissionsoftware 34 to transmit the calculated polynomial valuesP_(w)((α_(w))^(NbRepet-1-i)) to at least one other receiving station 10.The calculated polynomial values P_(w)((α_(w))^(NbRepet-1-i)) are forexample transmitted in the form of NbRepet data packets Paquet(i),0≦i≦NbRepet−1, transmitted successively.

The packets Pacquet(i) are for example defined as follows:Paquet(i)=P ₀((α₀)^(NbRepet-1-i))∥ . . . ∥P _(w)((α_(w))^(NbRepet-1-i))∥. . . ∥P _(v)((α_(v))^(NbRepet-1-i))  (5)

with NbRepet>1, 0≦i≦NbRepet−1, 0≦w≦v,

(α_(w))^(NbRepet-1-i) designating the predetermined respective value ofthe variable to calculate the corresponding polynomial value, and

∥ symbolizing a data concatenation.

During step 130, the or each receiving station 10 receives packets R_(m)containing said polynomial values P_(w)((α_(w))^(NbRepet-1-m)). Thisassumes that each receiving station 10 receives NbMot packets R₀, R₁, .. . , R_(NbMot-1), with the convention R_(m)=Paquet(t(m)), t(m)designating the reception moment of the packet R_(m), with 0≦m≦NbMot−1.

The or each receiving station 10 precisely knows the reception timedeviations between the different packets R₀, R₁, . . . , R_(NbMot-1).These time deviations are denoted d(n), 1≦n≦NbMot−1 and verify thefollowing equations:t(1)=t(0)+d(1),t(2)=t(1)+d(2), . . . ,t(NbMot−1)=t(NbMot−2)+d(NbMot−1)  (6)

In other words, the different reception moments t(m) are defined asfollows:

$\begin{matrix}{{t(m)} = {{t\left( {{NbMot} - 1} \right)} - {\sum\limits_{n = {m + 1}}^{{NbMot} - 1}{{d(n)}\mspace{14mu}{or}}}}} & (7) \\{{{{t(0)} = {{t\left( {{NbMot} - 1} \right)} - {d(1)} - {d(2)} - \ldots - {d\left( {{NbMot} - 1} \right)}}},{{t(1)} = {{t\left( {{NbMot} - 1} \right)} - {d(2)} - \ldots - {d\left( {{NbMot} - 1} \right)}}},\ldots\mspace{14mu},{{t\left( {{NbMot} - 2} \right)} = {{t\left( {{NbMot} - 1} \right)} - {d\left( {{NbMot} - 1} \right)}}},{and}}{t\left( {{NbMot} - 1} \right)}} & (8)\end{matrix}$

Each received packet R_(m) is then written in the following form:

$\begin{matrix}{{R_{0} = {{{Paquet}\left( {t(0)} \right)} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1 - {t{(0)}}} \right)}\mspace{11mu}{\mspace{14mu}\ldots\mspace{14mu} }\mspace{11mu}{P_{v}\left( \left( \alpha_{v} \right)^{{NbRepet} - 1 - {t{(0)}}} \right)}}}}{R_{1} = {{{Paquet}\left( {t(1)} \right)} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1 - {t{(1)}}} \right)}\mspace{11mu}{\mspace{14mu}\ldots\mspace{14mu} }\mspace{11mu}{P_{v}\left( \left( \alpha_{v} \right)^{{NbRepet} - 1 - {t{(1)}}} \right)}}}}} & (9) \\\begin{matrix}{{{{{\mspace{79mu}{{\ldots{R_{{{NbMot} - 1}\;} = {{{Paquet}\left( {t\left( {{NbMot} - 1} \right)} \right)} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}}} \right)}\mspace{11mu}{\mspace{14mu}\ldots\mspace{14mu} }\mspace{14mu}{P_{v}\left( \left( \alpha_{v} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}}} \right)}}}}}\mspace{79mu}{{which}\mspace{14mu}{is}\mspace{14mu}{rewritten}\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{form}\text{:}}{R_{0\;} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}} + {d{(1)}} + \ldots + {d{({{NbMot} - 1})}}} \right)}{\mspace{14mu}\ldots\mspace{14mu} }}}}\quad}{P_{v}\left( \left( \alpha_{v} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}} + {d{(1)}} + \ldots + {d{({{NbMot} - 1})}}} \right)}}{R_{1\;} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}} + {d{(2)}} + \ldots + {d{({{NbMot} - 1})}}} \right)}{\mspace{14mu}\ldots\mspace{14mu} }}}}\quad}{P_{v}\left( \left( \alpha_{v} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}} + {d{(2)}} + \ldots + {d{({{NbMot} - 1})}}} \right)}} \\{{{{{\mspace{79mu}{\ldots{R_{{{NbMot} - 2}\;} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}} + {d{({{NbMot} - 1})}}} \right)}{\mspace{14mu}\ldots\mspace{14mu} }}}}\quad}{P_{v}\left( \left( \alpha_{v} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}} + {d{({{NbMot} - 1})}}} \right)}}{R_{{{NbMot} - 1}\;} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}}} \right)}{\mspace{14mu}\ldots\mspace{14mu} }}}}\quad}{P_{v}\left( \left( \alpha_{v} \right)^{{NbRepet} - 1 - {t{({{NbMot} - 1})}}} \right)}}\end{matrix} & (10)\end{matrix}$

The time synchronization information t_final is defined by the equation:t_final=NbRepet−1−t(NbMot−1)  (11)

The second determination software 38 then determines, by Lagrangeinterpolation, v+1 polynomials Q_(w)(X) of degree NbMot−1, with 0≦w≦vand v≧1, using the following equation:

$\begin{matrix}{{Q_{w}(X)} = {{P_{w}\left( {\left( \alpha_{w} \right)^{t\_ final}X} \right)} = {\left( T_{NbMot} \right)_{w} + {\sum\limits_{j = 1}^{{NbMot} - 1}{\left( \alpha_{w} \right)^{{t\_ final} \times j} \times \left( T_{j} \right)_{w} \times X^{j}}}}}} & (12)\end{matrix}$

According to the preceding, the NbMot packets R₀, R₁, . . . ,R_(NbMot-1) are then written

R₀ = Q₀((α₀)^(d(1) + … + d(NbMot − 1)))    …    Q_(v)((α_(v))^(d(1) + … + d(NbMot − 1)))R₁ = Q₀((α₀)^(d(2) + … + d(NbMot − 1)))    …    Q_(v)((α_(v))^(d(2) + … + d(NbMot − 1)))     …     R_(NbMot − 2) = Q₀((α₀)^(d(NbMot − 1)))    …    Q_(v)((α_(v))^(d(NbMot − 1)))     R_(NbMot − 1) = Q₀(1)     …    Q_(v)(1)

In the described example embodiment, the coefficients of each polynomialQ_(w)(X) belong to the Galois field GF(2^(a(w))).

More specifically, the second determination software 38 then determinesthe v+1 following polynomials:

$\begin{matrix}{{Q_{0}(X)} = {\left( T_{NbMot} \right)_{0} + {{{CST}\left( \alpha_{0} \right)}^{t\_ final}X} + {\left( T_{2} \right)_{0}\left( \alpha_{0} \right)^{{t\_ final} \times 2}{\quad{{X^{2} + \ldots + {\left( T_{{NbMot} - 1} \right)_{0}\left( \alpha_{0} \right)^{{t\_ final} \times {({{NbMot} - 1})}}X^{{NbMot} - 1}{Q_{1}(X)}}} = {\left( T_{NbMot} \right)_{1} + {\left( T_{1} \right)_{1}\left( \alpha_{1} \right)^{t\_ final}X} + {\left( T_{2} \right)_{1}\left( \alpha_{1} \right)^{{t\_ final} \times 2}{\quad{{X^{2} + \ldots + {\left( T_{{NbMot} - 1} \right)_{1}\left( \alpha_{1} \right)^{{t\_ final} \times {({{NbMot} - 1})}}X^{{NbMot} - 1}\mspace{79mu}\ldots{Q_{v}( X)}}} = {\left( T_{NbMot} \right)_{v} + {\left( T_{1} \right)_{v}\left( \alpha_{v} \right)^{t\_ final} X} + {\left( T_{2} \right)_{v}\left( \alpha_{v} \right)^{{t\_ final} \times 2}{\quad{X^{2} + \ldots +}\quad}{\quad{\left( T_{{NbMot} - 1} \right)_{v}\left( \alpha_{v} \right)^{{t\_ final} \times {({{NbMot} - 1})}}X^{{NbMot} - 1}}}}}}}}}}}}}} & (13)\end{matrix}$

Each coefficient of the polynomial Q_(w)(X) for the term X^(j) of degreej is denoted Coeff(Q_(w)(X), j), and each polynomial Q_(w)(X) is thenwritten:

$\begin{matrix}{{Q_{w}(X)} = {\left( T_{NbMot} \right)_{w} + {\sum\limits_{j = 1}^{{NbMot} - 1}{{{Coeff}\left( {{Q_{w}(X)},j} \right)}X^{j}}}}} & (14)\end{matrix}$

The second calculation software 40 then calculates the timesynchronization information t_final using the coefficient Coeff(Q₀(X),1), the latter verifying, according to equations (12) and (14), thefollowing equation:Coeff(Q ₀(X),1)=(α₀)^(t) ^(_) ^(final)(T ₁)₀=(α₀)^(t) ^(_)^(final)CST  (15)

Consequently, the quantity (α₀)^(t) ^(_) ^(final) is found bycalculating the quantity Coeff(Q₀(X),1)/CST in the Galois fieldGF(2^(k)). The value k being relatively small, the second calculationsoftware 40 is then able to find the time synchronization informationt_final from the value (α₀)^(t) ^(_) ^(final), for example using a matchtable between the elements (α₀)^(m) and m, or via an exhaustive searchon the few possible values of the time synchronization informationt_final.

The receiving station 10 then knows, at the end of the transmission ofthe NbRepet−1 data packets Paquet(m) for example corresponding to asynchronization phase S, to position itself exactly on a successivecommunication phase F, as shown in FIG. 3. The communication phase F forexample allows the transmission of a useful information flow at the endof the synchronization phase S.

During step 150, the second determination software 38 lastly determinesthe value of each of the NbMot words T₁, T₂, . . . , T_(NbMot) from theLagrange interpolation of the received polynomial valuesP_(w)((α_(w))^(NbRepet-1-i)).

From the coefficients of each of the v+1 polynomials Q_(w)(X), 0≦w≦v,the second determination software 38 obtains the word T_(NbMot)equivalent to:T _(NbMot)=(T _(NbMot))₀∥(T _(NbMot))₁∥(T _(NbMot))₂∥ . . . ∥(T_(NbMot))_(v)  (16)

For the other words T_(j), 0≦j≦NbMot−1, the second determinationsoftware 38, knowing the value (α₀)^(t) ^(_) ^(final), determines eachpattern (T_(j))_(w) from each polynomial Q_(w)(X) using the followingequation:

$\begin{matrix}{\left( T_{j} \right)_{w} = \frac{{Coeff}\left( {{Q_{w}(X)},j} \right)}{\left( \alpha_{w} \right)^{{t\_ final} \times j}}} & (17)\end{matrix}$

the value of (α_(w))^(t) ^(_) ^(final) being calculated from the knownvalue of the primitive element α_(w) and the value of the timesynchronization information t_final previously calculated.

In other words, each word T_(j) is, according to equations (2) and (17),determined as follows:

$\begin{matrix}{T_{j} = {\frac{{Coeff}\left( {{Q_{0}(X)},j} \right)}{\left( \alpha_{0} \right)^{{t\_ final} \times j}}{{\frac{{Coeff}\left( {{Q_{1}(X)},j} \right)}{\left( \alpha_{1} \right)^{{t\_ final} \times j}}{{\ldots{\frac{{Coeff}\left( {{Q_{v}(X)},j} \right)}{\left( \alpha_{v} \right)^{{t\_ final} \times j}}}}}}}}} & (18)\end{matrix}$

As an example, the transmission method is described below in theparticular case where NbMot is equal to 2 and the integer number v isequal to 1.

The information that must be transmitted has a size of 2×N bits.Assuming that the constant value CST is located on the first k bits ofthe first word T1, the first and second words to be transmitted T₁, T₂are then written:T ₁=CST∥(T ₁)₁  (19)

where CST is an element of the Galois field GF(2^(k)) and (T₁)₁ is anelement of the Galois field GF(2^(N-k)), andT ₂=(T ₂)₀∥(T ₂)₁  (20)

where (T₂)₀ is an element of the Galois field GF(2^(k)) and (T₂)₁ is anelement of the Galois field GF(2^(N-k)).

The first determination software 30 then determines the following twopolynomials P₀(X) and P₁(X) of degree 1:P ₀(X)=(T ₂)₀+CST×XP ₁(X)=(T ₂)₁+(T ₁)₁ ×XP ₀(X)=(T ₂)₀+CST·XP ₁(X)=(T ₂)₁+(T ₁)₁ ·X  (21)

P₀(X) being defined in the Galois field GF(2^(k)) and P₁(X) beingdefined in the Galois field GF(2^(N-k)).

The transmitted NbRepet packets Paquet(i) are then the following:

$\begin{matrix}{{{Paquet}(0)} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 1} \right)}{{{{P_{1}\left( \left( \alpha_{1} \right)^{{NbRepet} - 1} \right)}{{Paquet}(1)}} = {{P_{0}\left( \left( \alpha_{0} \right)^{{NbRepet} - 2} \right)}{{{P_{1}\left( \left( \alpha_{1} \right)^{{NbRepet} - 2} \right)}\ldots{{{Paquet}\left( {{NbRepet} - 2} \right)} = {{P_{0}\left( \alpha_{0} \right)}{{{{P_{1}\left( \alpha_{1} \right)}{{Paquet}\left( {{NbRepet} - 1} \right)}} = {{P_{0}(1)}{{P_{1}(1)}}}}}}}}}}}}}} & (22)\end{matrix}$

In reception, it is then assumed that the receiving station 10 receivesNbMot packets, i.e., 2 packets R₀ and R₁, at respective moments t0 andt1, with t1 equal to t0+d, where d represents the time deviation betweenthe two received packets, that time deviation d being known by thereceiving station 10.

The first received packet R₀ verifies:R ₀=Paquet(t0)=P ₀((α₀)^(NbRepet-1-t0))∥P ₁((α₁)^(NbRepet-1-t0))   (23)which is written in the formR ₀ =P ₀((α₀)^(NbRepet-1-t1)(α₀)^(d))∥P ₁((α₁)^(NbRepet-1-t1)(α₁)^(d))=Q₀((α₀)^(d))∥Q ₁((α₁)^(d))   (24)given thatt1=t0+d   (25)

The second received packet R₁ verifies:R ₁=Paquet(t1)=P ₀((α₀)^(NbRepet-1-t1))∥P ₁((α₁)^(NbRepet-1-t1))   (26)which is written in the formR ₁ =P ₀((α₀)^(NbRepet-1-t1)(α₀)⁰)∥P ₁((α₁)^(NbRepet-1-t1)(α₁)⁰)=Q₀(1)∥Q ₁(1)   (27)

The receiving station 10 reconstructs the polynomials by Lagrangeinterpolation:Q ₀(X)=Coeff(Q ₀(X),0)+Coeff(Q ₀(X),1)×X=P ₀((α₀)^(NbRepet-1-t1)×X)  (28)Q ₁(X)=Coeff(Q ₁(X),0)+Coeff(Q ₁(X),1)×X=P ₁((α₁)^(NbRepet-1-t1)×X)  (29)

The receiving station 10 deduces, by polynomial identification, thatT ₂=Coeff(Q ₀(X),0)∥Coeff(Q ₁(X),0)   (30)and thatCoeff(Q ₀(X),1)=(α₀)^(NbRepet-1-t1)(T ₁)₀=(α₀)^(NbRepet-1-t1)CST   (31)then thatCoeff(Q ₁(X),1)=(α₁)^(NbRepet-1-t1)(T ₁)₁   (32)

The receiving station 10 then deduces the value of NbRepet−1−t1 fromequation (31), then the value of the pattern (T₁)₁ from the followingequation (32):

$\begin{matrix}{\left( T_{1} \right)_{1} = \frac{{Coeff}\left( {{Q_{1}(X)},1} \right)}{\left( \alpha_{1} \right)^{{NbRepet} - 1 - {t\; 1}}}} & (33)\end{matrix}$

The transmission method and the transmission network according to thedescribed technology makes it possible to transmit the informationcomprising the data words T₁, . . . , T_(nbMot), between a transmittingstation 10 and one or more receiving stations 10 via the transmission ofonly NbRepet data packets Paquet(i), while guaranteeing the desiredquality of service.

As a comparison, for a same quality of service and for a same size ofthe transmitted packets, the transmission method according to thedescribed technology requires a number of transmitted packetsapproximately 2.5 times lower than the number of transmitted packetsnecessary with the standard transmission method.

Furthermore, the transmission method according to the describedtechnology also makes it possible to calculate the time synchronizationinformation t_final quite simply.

One can thus see that the transmission method and network according tothe described technology makes it possible to reduce the quantity ofdata transmitted by the transmitting station to the receivingstation(s), to convey said information comprising the data words T₁, . .. , T_(nbMot), while offering the same quality of service as thetransmission method of the state of the art.

The transmission network according to the invention is thus particularlyfaster for transmitting the information.

While there have been shown and described and pointed out thefundamental novel features of the invention as applied to certaininventive embodiments, it will be understood that the foregoing isconsidered as illustrative only of the principles of the invention andnot intended to be exhaustive or to limit the invention to the preciseforms disclosed. Naturally, modifications and variations are within thescope of the invention as determined by the appended claims wheninterpreted in accordance with the breadth to which they are entitled.

What is claimed is:
 1. A method for transmitting information between aplurality of radioelectric stations, each of the radioelectric stationscomprising a transmitter and a receiver, the information comprisingNbMot words of data, NbMot being an integer strictly greater than 1, themethod comprising: determining at least one polynomial of degreeNbMot−1, each of the NbMot coefficients of the polynomial correspondingto a respective one of the words, the polynomial having a variable;calculating NbRepet polynomial values for the polynomial, NbRepet beingan integer strictly greater than 1, each of the polynomial values beingcalculated for a respective predetermined value of the variable;transmitting the calculated polynomial values from a first radioelectricstation to at least one second radioelectric station, wherein NbRepetdata packets are successively transmitted during the transmission;receiving polynomial values by the second radioelectric station;determining, via the second radioelectric station, the words from aLagrange interpolation of the received polynomial values; andcalculating, via the second radioelectric station receiving the packets,time synchronization information for time synchronizing with the firstradioelectric station transmitting the packets, from the receivedpolynomial values and reception time deviations between the differentreceived packets.
 2. The method according to claim 1, wherein each ofthe words is divided into a plurality of patterns, and wherein severalof the polynomials are determined using the following equation:${P_{w}(X)} = {\left( T_{NbMot} \right)_{w} + {\sum\limits_{j = 1}^{{NbMot} - 1}{\left( T_{j} \right)_{w} \times X^{j}}}}$with NbMot>1, 0≦w≦v and v≧1, j being an index designating a respectiveone of the words and X designating the variable.
 3. The method accordingto claim 1, wherein the packets are defined as follows:Paquet(i)=P ₀((α₀)^(NbRepet-1-i))∥ . . . ∥P _(w)((α_(w))^(NbRepet-1-i))∥. . . ∥P _(v)((α_(v))^(NbRepet-1-i)) with NbRepet>1, 0≦i≦NbRepet−1,0≦w≦v, P_(w) designating a respective polynomial, (αw)NbRepet−1-idesignating the predetermined respective value of the variable tocalculate the corresponding polynomial value, and ∥ symbolizing a dataconcatenation.
 4. The method according to claim 1, wherein the datawords each have the same size equal to N bits, N being an integerstrictly greater than
 1. 5. The method according to claim 4, wherein oneword of the data words comprises k bit(s) having a predeterminedconstant value, k being an integer with 1≦k≦N.
 6. The method accordingto claim 1, wherein each of the words comprises at least one pattern,and wherein the pattern represents an element of a mathematical field.7. The method according to claim 6, wherein each of the respectivepredetermined values for which a polynomial value is calculated is aprimitive element of the Galois field.
 8. A network for transmittinginformation, the network comprising a plurality of radioelectricstations, each of the radioelectric stations comprising a transmitterand a receiver, the information comprising NbMot words of data, NbMotbeing an integer strictly greater than 1, wherein each of theradioelectric stations designed to transmit the information furthercomprises: means for determining at least one polynomial of degreeNbMot−1, each of the NbMot coefficients of the polynomial correspondingto a respective one of the words, the polynomial having a variable;means for calculating NbRepet polynomial values for the polynomial,NbRepet being an integer strictly greater than 1, each of the polynomialvalues being calculated for a respective predetermined value of thevariable; and means for transmitting the calculated polynomial values toat least one other radioelectric station, wherein each of the stationsdesigned to receive the information further comprises: means forreceiving the polynomial values; means for determining the words from aLagrange interpolation of the received polynomial values; means forcalculating time synchronization information for time synchronizing withthe station designed to transmit the information, from the receivedpolynomial values; and reception time deviations between differentreceived packets, the station designed to transmit the informationconfigured to successively transmit NbRepet data packets.